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Date May 2013 Marks available 7 Reference code 13M.2.sl.TZ1.7
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 7 Adapted from N/A

Question

A random variable XX is normally distributed with μ=150μ=150 and σ=10σ=10 .

Find the interquartile range of XX .

Markscheme

recognizing one quartile probability (may be seen in a sketch)     (M1)

eg   P(X<Q3)=0.75P(X<Q3)=0.75 , 0.250.25

finding standardized value for either quartile     (A1)

eg   z=0.67448z=0.67448 , z=0.67448z=0.67448

attempt to set up equation (must be with zz-values)     (M1)

eg   0.67=Q3150100.67=Q315010 , 0.67448=x150100.67448=x15010

one correct quartile

eg   Q3=156.74Q3=156.74 , Q1=143.25Q1=143.25

correct working     (A1)

eg   other correct quartile, Q3μ=6.744Q3μ=6.744

valid approach for IQR (seen anywhere)     (A1)

eg   Q3Q1Q3Q1 , 2(Q3μ)2(Q3μ)

IQR =13.5=13.5     A1     N4

[7 marks]

Examiners report

This was an accessible problem that created difficulties for candidates. Although they recognized and often wrote down a formula for IQR, most did not understand the conceptual nature of the first and third quartiles. Those who did could solve the problem effectively using their GDC in relatively few steps. Candidates that were able to start this question often drew the normal curve and gave quartile values at 140140 and 160160. This generally led to a solution which while wrong, was also clearly inadequate for the indicated 7 marks.

Syllabus sections

Topic 5 - Statistics and probability » 5.9 » Normal distributions and curves.
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